Riven
Riven is broken when played mechanically well. Nothing you can do. R-Q-AA-Q-AA-Hydra-AA-W-AA-Q-R in the same time it takes someone new to Riven to perform R-QQQ-Hydra-W-R. The first will 100-0 your Mundo in seconds and the second will be beaten by just about anything. Problem with nerfing her is that you kill her overall viability for those not mechanically great. Riot needs to shift all her power from her auto attacks (her main source of damage) into her abilities to remove this huge mechanical gap while also hitting her mobility.
Katarina
The only thing truly broken about Katarina is her passive and itemization. She's two extremes;
- Dive in, press R and hope you don't get a CC heading your way.
- Become the cleanup crew after or towards the end of a team fight.
The largest issue is itemization for Katarina. Hybrids became a thing of the past because AP and AD will never be equal both in price and ratios, so one will always be statistically better.
Katarina is the last of the line of Hybrid champions and no item works for her ideally. Gunblade? Active scales off of AP and if you build AP, your Sinister Steel and auto attacks become almost pointless. Lichbane? Same problem as Gunblade. Rageblade? Pointless. She channels her ultimate.
Building full AP forces you towards this all-in ultimate or nothing while making part of your kit useless.
Building full AD is the exact same but making your Bouncing Blades useless and your Shunpo do no damage.
Doing nothing and cleaning up safely afterwards is unreliable.
There is no middle ground. The store needs more hybrid items (unlikely) or Katarina needs shoving towards one of the two so that she can utilize ALL of her kit instead of the vast majority of damage output coming from her R.
Now, for the passive. This is an issue because it cannot be balanced in the traditional sense. It isn't like you can reduce/increase range, damage, cooldowns like a normal ability. This passive allows a fed Katarina to become unstoppable because a single kill will chain to an ace if you're all within a 700 range from each other (her maximum Shunpo range). This passive needs removing and her cooldowns need lowering dramatically to make up for it.
Katarina was built on what worked at the time of her creation, yet there was no thought of where you could balance her should she require it. This is why there are two fundamental issues with Katarina (One that appeared over time: itemization and an old passive that clashes with the balance standards today) and why a rework to her entire kit or her ratios is highly probable.